Can we solve this equation without choices ?
9^x-8^x=3
Yes , graphically....
or use an iterative method, for example...
$\displaystyle x_{n+1}=x_n-\frac{9^{x_n}-8^{x_n}-3}{9^{x_n}\ln 9 -8^{x_n} \ln 8}$
Starting with $\displaystyle x_o=1$
$\displaystyle x_5=1.367251988$
$\displaystyle x_6=1.367251981$
The above uses Newton's method.